There’s actually this concept known as utility in economics.It’s the value of something changesdepending on how much money is in your wallet, for example,and how much you’re willing to lose.And what Kelly did is he looked at these two contrastingaims you have, if you want to give a good long-term return.First you’re trying to make money, because you’vegot a biassed bet.But you’re also trying to avoid going bankrupt.Essentially you’re still tossing a coin.There’s that chance you’re going to lose.I don’t think anyone here would have bet their house on this.Maybe you would have.You might have an angry family.But in this case, you want to somehow exploit it, but alsolimit your losses.And what Kelly did was come up with this formula.So I apologise for my handwriting.Basically you’ve got the odds, which in this case is two.You got the probability you’ll win– this Pwin–minus the probability you’ll lose.And this is the optimal fraction of your moneyto bet for a given edge over somebody in a wager situation.So the bet I just showed you. Learn more about game bankruptcy onĀ CasinoSlots.

The odds were two.The probability you’ll win is a half, because it’s a coin toss.Probability you’ll lose is also a half.So if you stick these numbers in,you get the following kind of equation.A little bit of arithmetic– you can end up with a quarter.So in this situation, if you want to maximise your long-termgrowth of money, it’s optimal to risk about a quarterof your income.Just have a think back to when you were raisinghands, whether that was the course of–were you taking advantage or not?Now some of you might think, OK, that’s all well and good.You showed me a formula.Let’s test it out.Now I could have, of course, adopt the Karl Pearson approachand spend the next half an hour or so tossing coinsto convince you.That’s a bit boring.So what I thought I’d do instead is show yousome simulations of if we adopteddifferent strategies, what kind of outcomes we would get.So here along the vertical is your bankroll.I’m going to assume that you start with a hundred pounds.

And along the bottom is the coin flips.So we’re going to play this bet again,and again, and again, and see whatyou’d end up with over time.Now you might have thought a quarter of my money, that’snot taking risks.So I want to go big.You might say, well, I want to bet 80% of my money.And in this case, if we just do one random simulation, whatmight happen is you’ll get a couple of big winsat the start.You’re approaching a thousand pounds.Lose a load of money– win a load of money.It’s exciting.And then lose all your money and go bankrupt–Less exciting.If you adopt this optimal Kelly strategyand bet 25%, what will happen is it will take longer.You’ll grow a bit slow over time.But you won’t go bankrupt.And actually in the long term, youwill get something that takes off.You might say actually, that’s still a bit too much for me.I’m going to bet 10% of my incomeon each one of these wages.And in this case, if you do it randomly,it’ll take a long time to grow.So you won’t go bankrupt.